“Möbius Transformations Revealed is a wonderful video clarifying a deep topic. This is amazing work by Douglas Arnold and Jonathan Rogness of the University of Minnesota.”

— Edward Tufte

Möbius Transformations Revealed is a short video by
Douglas Arnold and
Jonathan Rogness
which depicts the beauty of Möbius transformations and shows how moving to a higher dimension reveals their essential unity. It was one of the winners
in the 2007 Science
and Engineering Visualization Challenge and was featured along with the other
winning entries in the September 28, 2007 issue of journal Science.
The video, which was first released on YouTube in June 2007, has been
watched there by nearly two million viewers and classified
as a “Top Favorite of All Time“ first in the Film & Animation category and later in the Education category.
It was selected for inclusion in the MathFilm 2008 DVD, published
by Springer.

Möbius Transformations Revealed was built primarily
using POV-Ray with some help from
Mathematica. The soundtrack is a performance of "Von fremden Ländern und Menschen"
("Of Foreign Lands and Peoples")
from Robert Schumann's Kinderszenen, Op. 15. The pianist is Donald Betts.